Filter by: Content type: ALL Problems Articles Games Stage: All Stage 1&2 Stage 2&3 Stage 3&4 Stage 4&5 Challenge level:
Arrange the shapes in a line so that you change either colour or shape in the next piece along. Can you find several ways to start with a blue triangle and end with a red circle?
Are all the possible combinations of two shapes included in this set of 27 cards? How do you know?
This activity investigates how you might make squares and pentominoes from Polydron.
Can you order pictures of the development of a frog from frogspawn and of a bean seed growing into a plant?
How many different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?
Make your own double-sided magic square. But can you complete both sides once you've made the pieces?
There is a long tradition of creating mazes throughout history and across the world. This article gives details of mazes you can visit and those that you can tackle on paper.
An activity making various patterns with 2 x 1 rectangular tiles.
Can you see who the gold medal winner is? What about the silver medal winner and the bronze medal winner?
What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?
How many ways can you find of tiling the square patio, using square tiles of different sizes?
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.
Using the statements, can you work out how many of each type of rabbit there are in these pens?
Let's say you can only use two different lengths - 2 units and 4 units. Using just these 2 lengths as the edges how many different cuboids can you make?
How many different ways can you find of fitting five hexagons together? How will you know you have found all the ways?
A merchant brings four bars of gold to a jeweller. How can the jeweller use the scales just twice to identify the lighter, fake bar?
This magic square has operations written in it, to make it into a maze. Start wherever you like, go through every cell and go out a total of 15!
In a square in which the houses are evenly spaced, numbers 3 and 10 are opposite each other. What is the smallest and what is the largest possible number of houses in the square?
In how many ways could Mrs Beeswax put ten coins into her three puddings so that each pudding ended up with at least two coins?
Start with three pairs of socks. Now mix them up so that no mismatched pair is the same as another mismatched pair. Is there more than one way to do it?
El Crico the cricket has to cross a square patio to get home. He can jump the length of one tile, two tiles and three tiles. Can you find a path that would get El Crico home in three jumps?
Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.
Find your way through the grid starting at 2 and following these operations. What number do you end on?
Place the 16 different combinations of cup/saucer in this 4 by 4 arrangement so that no row or column contains more than one cup or saucer of the same colour.
Using different numbers of sticks, how many different triangles are you able to make? Can you make any rules about the numbers of sticks that make the most triangles?
Can you cover the camel with these pieces?
What happens when you try and fit the triomino pieces into these two grids?
If we had 16 light bars which digital numbers could we make? How will you know you've found them all?
In this town, houses are built with one room for each person. There are some families of seven people living in the town. In how many different ways can they build their houses?
Find all the numbers that can be made by adding the dots on two dice.
In a bowl there are 4 Chocolates, 3 Jellies and 5 Mints. Find a way to share the sweets between the three children so they each get the kind they like. Is there more than one way to do it?
In this challenge, buckets come in five different sizes. If you choose some buckets, can you investigate the different ways in which they can be filled?
How could you put eight beanbags in the hoops so that there are four in the blue hoop, five in the red and six in the yellow? Can you find all the ways of doing this?
Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?
This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!
Can you find which shapes you need to put into the grid to make the totals at the end of each row and the bottom of each column?
In the planet system of Octa the planets are arranged in the shape of an octahedron. How many different routes could be taken to get from Planet A to Planet Zargon?
Moira is late for school. What is the shortest route she can take from the school gates to the entrance?
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
How many trains can you make which are the same length as Matt's, using rods that are identical?
My coat has three buttons. How many ways can you find to do up all the buttons?
Try out the lottery that is played in a far-away land. What is the chance of winning?
How many DIFFERENT quadrilaterals can be made by joining the dots on the 8-point circle?
There are 4 jugs which hold 9 litres, 7 litres, 4 litres and 2 litres. Find a way to pour 9 litres of drink from one jug to another until you are left with exactly 3 litres in three of the jugs.
Investigate the different ways you could split up these rooms so that you have double the number.
This problem focuses on Dienes' Logiblocs. What is the same and what is different about these pairs of shapes? Can you describe the shapes in the picture?
You cannot choose a selection of ice cream flavours that includes totally what someone has already chosen. Have a go and find all the different ways in which seven children can have ice cream.
Nina must cook some pasta for 15 minutes but she only has a 7-minute sand-timer and an 11-minute sand-timer. How can she use these timers to measure exactly 15 minutes?